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SAN FRANCISCO — Google’s second-quarter profit quadrupled as the online search leader continued to exceed the great expectations underlying its soaring stock, but apparently it still wasn’t good enough for investors demanding even more outlandish growth.

The company said yesterday that it earned $342.8 million, or $1.19 per share, for the three months ended in June. The results compared with net income of $79.1 million, or 30 cents per share, at the same time last year.

If not for a charge to account for employee-stock options issued before Google went public 11 months ago, the earnings would have ranged between $1.29 and $1.35 per share. That topped the mean estimate of $1.21 per share among analysts surveyed by Thomson Financial.

Revenue for the period totaled $1.38 billion, nearly doubling from $700.2 million last year. After subtracting the commissions that Google paid to other Web sites in its advertising network, the revenue stood at $890 million, beating the Wall Street estimate of $842 million, according to Thomson Financial.

The company released its results after the stock market closed yesterday. Reflecting investor anticipation of a big quarter, Google’s shares reached a new high of $317.80 before retreating slightly to finish at $313.94, up $1.94 for the day.

But then the shares dropped $17.95, or 5.7 percent, in extended trading as investors apparently fretted about a slowdown in the company’s growth.

The negative reaction didn’t surprise Piper Jaffray analyst Safa Rashtchy. “The stock had been going up too much in the last few days. It was becoming too much about a game of momentum. This quarter looked fine to me.”

Although Google’s earnings and revenue continue to rise at a rapid clip, some of the gains weren’t quite as large as in recent quarters — something that often happens as companies get bigger and the comparisons become tougher.

In another development that may have troubled investors, Google’s second-quarter revenue rose by 10 percent from the previous quarter. The sequential revenue growth had ranged between 15 percent and 28 percent in the previous three quarters that Google had reported as a publicly held company.

In a conference call with analysts yesterday, Google Chief Financial Officer George Reyes told analysts he expected it be even more difficult for the company to maintain its growth pace in the third quarter, and not just because people won’t be in front of their computers as much during the summer.

Google says its results during last year’s third quarter were boosted by the intense media coverage that surrounded its initial public offering of stock last August.

Besides the caveat about the third quarter, Google management sounded mostly bullish about its prospects. “Business is going quite well,” CEO Eric Schmidt said yesterday. “Things aren’t falling off a cliff.”

Google is under immense pressure to produce extraordinary earnings growth because of how high its stock has climbed since the company’s IPO at $85 per share.

Although Google co-founders Larry Page and Sergey Brin have stressed they aren’t interested in meeting short-term expectations, the company still has surpassed analysts’ estimates in each quarter since the IPO.

The stellar showing has propelled Google’s market value to nearly $90 billion in less than seven years in business.